30 lines
918 B
Text
30 lines
918 B
Text
-- Copyright (c) 2014 Floris van Doorn. All rights reserved.
|
||
-- Released under Apache 2.0 license as described in the file LICENSE.
|
||
-- Author: Floris van Doorn
|
||
|
||
import .basic .constructions
|
||
|
||
open eq eq.ops category functor category.ops prod
|
||
|
||
namespace yoneda
|
||
--representable functor
|
||
section
|
||
parameters {ob : Type} {C : category ob}
|
||
set_option pp.universes true
|
||
check @type_category
|
||
section
|
||
parameters {a a' b b' : ob} (f : @hom ob C a' a) (g : @hom ob C b b')
|
||
-- definition Hom_fun_fun :
|
||
end
|
||
definition Hom : Cᵒᵖ ×c C ⇒ type :=
|
||
@functor.mk _ _ _ _ (λ a, hom (pr1 a) (pr2 a))
|
||
(λ a b f h, pr2 f ∘ h ∘ pr1 f)
|
||
(λ a, funext (λh, !id_left ⬝ !id_right))
|
||
(λ a b c g f, funext (λh,
|
||
show (pr2 g ∘ pr2 f) ∘ h ∘ (pr1 f ∘ pr1 g) = pr2 g ∘ (pr2 f ∘ h ∘ pr1 f) ∘ pr1 g, from sorry))
|
||
--I'm lazy, waiting for automation to fill this
|
||
|
||
|
||
|
||
end
|
||
end yoneda
|